Stability of cubic and quartic rho-functional inequalities in fuzzy normed spaces

Abstract

In this paper, we solve the following cubic rho-functional inequality

N(f (2x + y) + f (2x y) - 2f (x + y) 2 f (x y) 12 f (x) (1)

- rho (4f (x + y/2) + 4f (x - y/2) - f(x + y) - f(x - y) - 6f (x)),t) >= t/t + phi(x, y)

and the following quartic rho-functional inequality

N(f (2x + y) + f (2x y) 4f (x + y) 4f (x y) - 24 f (x) + 6f (y) (2)

-rho(8f (x + + 8f (x 2 f (x + y) 2 f (x y) 12 f (x) + 3 f (y)),t) >= t/t + phi(x, y)

in fuzzy normed spaces, where rho is a fixed real number with rho not equal 2.

Using the direct method, we prove the Hyers-Ulam stability of the cubic rho-functional inequality (1) and the quartic rho-functional inequality (2) in fuzzy Banach spaces.